# Takes a tape representing a natural number k (see Boolos, Burgess
# and Jeffrey for definition) and returns a tape representing a pair
# <k,k>.

(0,1, ,1,r)   
(0, , ,99,r)   
(1, , ,2,r)    # Look for blank
(1,1,1,1,r)   
(2, ,1,3,r)    # Wrote my 1.
(2,1,1,2,r)   
(3, , ,4,r)   
(3,1, ,5,r)   
(4, ,1,6,l)   
(5, ,1,7,r)   
(5,1,1,5,4)   
(6, , ,8,l)   
(6,1,1,6,l)   
(7, ,1,6,l)   
(8, , ,9,l)   
(8,1,1,8,l)   
(9, , ,0,r)   
(9,1,1,9,l)   

(9,1,1,1000,r)   # Former halt state.
(8,1,1,1000,r)   # Former halt state.
(7,1,1,1000,r)   # Former halt state.
(6,1,1,1000,r)   # Former halt state.
(5,1,1,1000,r)   # Former halt state.
(4,1,1,1000,r)   # Former halt state.
(2,1,1,1000,r)   # Former halt state.
(1,1,1,1000,r)   # Former halt state.
(99, , ,1000,r)   # Former halt state.
(99,1,1,1000,r)   # Former halt state.
# Skip this block of one's, goto next

(100,1,1,100,r)   
(100, , ,101,r)   
(101, , ,101,r)   
(101,1,1,102,l)   
(102, , ,103,r)   

(1000, , ,100,l)   #Goto start state, machine skip
(1000,1,1,100,l)   #Goto start state, machine skip

(1000,1,1,1001,r)  # Former halt state.
(102,1,1,1001,r)  # Former halt state.
(103, , ,1001,r)  # Former halt state.
(103,1,1,1001,r)  # Former halt state.
(99,1,1,1001,r)  # Former halt state.
# Takes a tape representing a natural number k (see Boolos, Burgess
# and Jeffrey for definition) and returns a tape representing a pair
# <k,k>.

(104,1, ,105,r)  
(104, , ,199,r)  
(105, , ,106,r)   # Look for blank
(105,1,1,105,r)  
(106, ,1,107,r)   # Wrote my 1.
(106,1,1,106,r)  
(107, , ,108,r)  
(107,1, ,109,r)  
(108, ,1,110,l)  
(109, ,1,111,r)  
(109,1,1,109,4)  
(110, , ,112,l)  
(110,1,1,110,l)  
(111, ,1,110,l)  
(112, , ,113,l)  
(112,1,1,112,l)  
(113, , ,104,r)  
(113,1,1,113,l)  

(1001, , ,104,l)  #Goto start state, machine double
(1001,1,1,104,l)  #Goto start state, machine double